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viscomp/viscomp.tex
@@ -233,7 +233,7 @@ \subsection{Fourier Transform}
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F(u,v) &= \frac{1}{N} \sum^{N-1}_{x=0} \sum^{N-1}_{y=0} f(x,y) \cdot e^{-i2\pi (\frac{ux+vy}{N})} \mathop{dx}\mathop{dy} \\
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f(x,y) &= \iint_{\mathbb{R}^2} F(u,v) \cdot e^{i 2\pi (ux+vy)} \mathop{du}\mathop{dv} \tag{inverse}
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\end{align*}
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- \( e^{-i2\pi (ux+vy)} = \cos (2\pi (ux+vy)) + i \cdot \sin(2\pi (ux + vy)) \)
+ \( e^{-i2\pi (ux+vy)} = \cos (2\pi (ux+vy)) - i \cdot \sin(2\pi (ux + vy)) \)
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\end{mainbox}
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Relevant trigonometric properties:
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\[\cos(x) = \frac{e^{ix} + e^{-ix}}{2},\; \sin(x) = \frac{e^{ix}-e^{-ix}}{2} \]
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